1. Field of the Invention
The present invention relates to an exponential function generator which generates an exponential function signal to produce linearly variable gains and a variable gain amplifier using the same.
2. Description of the Related Art
In a Radio Frequency (RF) receiver with its flexible transmission environment, an input signal is variable in a wide range whereas an output signal needs to be in a uniform magnitude as a uniform magnitude of signal is required at the demodulation end. Thus, the RF receiver is used with an automatic gain control system which regulates the magnitude of the signal.
FIG. 1 illustrates a basic concept of an automatic gain control system. The automatic gain control system amplifies an input signal Vin by a variable gain amplifier 11 while detecting the magnitude of an output signal Vout by a peak detector 12 and then compares the detected magnitude with a reference value VREF to generate a control signal Vc corresponding to the difference to vary the gain of the variable gain amplifier 11, so that the output signal Vout maintains a predetermined magnitude.
Such an automatic gain control system is composed of a negative feedback circuit in which a time constant changes in accordance with the gain of the variable gain amplifier 11, and thus is difficult to be maintained stably.
In order to solve such a problem, the gain of the variable gain amplifier 11 needs to be varied in a linear form per decibel (dB) in accordance with the control signal. Accordingly, the variable gain amplifier 11 of the automatic gain control system needs to be configured to provide exponential voltage gains in accordance with the control signal Vc applied. The variable gain amplifier 11 adopts multistage-connected current amplifiers (not shown) in which the gain is varied in proportion to a bias current, configured to exponentially vary the bias current of the current amplifier in accordance with the gain control signal Vc. Here, the means for converting the control signal into a current signal of an exponential function is called an exponential function generator.
The basic structure of an exponential function generator is illustrated in FIG. 2a. The circuit shown in FIG. 2a adopts the Bipolar Junction Transistor (BJT), utilizing its exponential current characteristics, which can be represented by following Equation 1.
                                          I                          C              ⁢                                                          ⁢              1                                =                                    I              S                        ⁢                          ⅇ                                                V                                      BE                    ⁢                                                                                  ⁢                    1                                                                    V                  T                                                                    ⁢                                  ⁢                              I                          C              ⁢                                                          ⁢              2                                =                                    I              S                        ⁢                          ⅇ                                                V                                      BE                    ⁢                                                                                  ⁢                    2                                                                    V                  T                                                                    ⁢                                  ⁢                                            V                              BE                ⁢                                                                  ⁢                1                                      -                          V                              BE                ⁢                                                                  ⁢                2                                              =                                    V              C                        -                          V              ref                                      ⁢                                  ⁢                                            I                              C                ⁢                                                                  ⁢                1                                                    I                              C                ⁢                                                                  ⁢                2                                              =                                    e              ⁢                                                                    V                                          BE                      ⁢                                                                                          ⁢                      1                                                        -                                      V                                          BE                      ⁢                                                                                          ⁢                      2                                                                                        V                  T                                                      =                          ⅇ                                                                    V                    C                                    -                                      V                    ref                                                                    V                  T                                                                                        Equation        ⁢                                  ⁢        1            
As shown in Equation 1, the currents IC1 and IC2 are generated exponentially according to the control voltage. In this structure, however, the temperature voltage VT is affected by the temperature, and thus requires an appropriately designed temperature compensation circuit. Also, the usable voltage range in this structure is very low in the tens of mV, with an attendant drawback of requiring an additional circuit for regulating the voltage level. This type of variable gain amplifier is explained in U.S. Pat. No. 6,259,321(entitled “CMOS Variable Gain Amplifier and Control Method therefore”).
An alternative form of exponential function generator uses Taylor series expansion as shown in following Equation 2.
                              exp          ⁡                      (            ax            )                          ≈                  1          +                                    a                              1                !                                      ⁢            x                    +                                                    a                2                                            2                !                                      ⁢                          x              2                                +          …          +                                    a              n                                      n              !                                +          …                                    Equation        ⁢                                  ⁢        2            
The above Equation 2 can be approximated to
            exp      ⁡              (        ax        )              ≈          1      +                        a                      1            !                          ⁢        x            +                                    a            2                                2            !                          ⁢                  x          2                      ,when |X|<<1. The exponential function generator using the Taylor Series expansion takes a form of circuit with the constant term, the proportional term, and the square term in Equation 2.
For the exponential function generator shown in FIG. 2b, the output current Iout is represented by following Equation 3.
                              I          out                =                                            2              ⁢                              I                0                                      +                                          K                1                            ⁢                              I                in                                      +                                                            K                  2                  2                                ⁢                                  I                  in                  2                                                            8                ⁢                                  I                  0                                                              =                      2            ⁢                                          I                0                            ⁡                              [                                  1                  +                                                                                    K                        1                                            2                                        ⁢                                                                  I                        in                                                                    I                        0                                                                              +                                                                                    K                        2                        2                                            16                                        ⁢                                                                  (                                                                              I                            in                                                                                I                            0                                                                          )                                            2                                                                      ]                                                                        Equation        ⁢                                  ⁢        3            
In Equation 3, Io is a bias current, Iin is an input current which is a current value converted from the control voltage outputted from a GM cell 21, and K1 is the gain of a transfer function 22.
The exponential function generator using the above Taylor Series expansion requires a square circuit as shown, and also needs to satisfy Iin<<Io.
Yet another alternative form of exponential function generator uses a pseudo-exponential function as follows.
                    exp        ⁡                  (                      2            ⁢            x                    )                    ≈                        1          +          x                          1          -          x                      ,                  ⁢    if                    x              ⁢          〈              〈        1            
FIG. 2c illustrates an exponential function generator employing the pseudo-exponential function. In the circuit shown in FIG. 2c, the output value VDS2 obtained is represented by an exponential function of an input current Iin as shown in the following equation.
                              V                      DS            ⁢                                                  ⁢            2                          =                                            2              ⁢                                                K                  p                                ⁡                                  (                                                            V                      DD                                        -                                                                                        V                        TP                                                                                                    )                                                                    K              n                                ⁢                                                    I                b                            +                              I                in                                                                    I                b                            -                              I                in                                                                            =                                            2              ⁢                                                K                  p                                ⁡                                  (                                                            V                      DD                                        -                                                                                        V                        TP                                                                                                    )                                                                    K              n                                ⁢                                    1              +                                                I                  in                                /                                  I                  b                                                                    1              -                                                I                  in                                /                                  I                  b                                                                                            =                                            2              ⁢                                                K                  p                                ⁡                                  (                                                            V                      DD                                        -                                                                                        V                        TP                                                                                                    )                                                                    K              n                                ⁢                      exp            ⁡                          (                              2                ⁢                                                      I                    in                                                        I                    b                                                              )                                          
However, this type of exponential function generator has to satisfy x<<1, i.e., Iin<<Ib. Also for this type, it is important to establish an appropriate operating point.
Other than the above types, there is an exponential function generator adopting a digital method in which a look-up table with exponential functions corresponding to the output value in proportion to the input value is provided. Then the data of the exponential function produced from the look-up table is converted into analogue signals (current or voltage) simply through a digital-analogue converter. But this type requires both the digital circuit and the analogue circuit, and plus the analogue-digital converter (ADC) and the digital-analogue converter (DAC), resulting in a complicated structure.
As described above, each type of conventional exponential function generator has drawbacks. Therefore, there needs to be researches on an exponential function generator which is not burdened with the use of BJT in the CMOS process, without limitations in the physical properties of the square circuit or the elements, and embodied through only an analogue method so as not to be complicated in its configuration.